Conformal field theories and compact curves in moduli spaces

Abstract

We show that there are many compact subsets of the moduli space $M_g$ of Riemann surfaces of genus $g$ that do not intersect any symmetry locus. This has interesting implications for $\mathcal{N}=2$ supersymmetric conformal field theories in four dimensions.

Update acknowledging recent developments

References in corpus (1)

• Anomalies involving the space of couplings and the Zamolodchikov metric

Cited by in corpus (4)

• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Anomalies of Duality Groups and Extended Conformal Manifolds
• Interface entropy in four dimensions as Calabi's diastasis on the conformal manifold
• Global aspects of moduli spaces of 2d SCFTs